%I #31 Jan 04 2022 21:52:02
%S 3,7,13,19,31,37,43,61,67,73,79,109,127,139,151,199,277,313,433,457,
%T 547,613,619,643,739,967
%N Prime numbers p such that (2^p + 1)/3 can be written in the form a^2 + 3*b^2.
%C These (2^p + 1)/3 numbers have no prime factors of the form 2 (mod 3) to an odd power.
%H Samuel S. Wagstaff, Jr., The Cunningham Project, <a href="http://homes.cerias.purdue.edu/~ssw/cun/">Factorizations of 2^n-1, for odd n's < 1200</a>
%o (PARI) forprime(i=2, 100, a=factorint(2^i+1)~; has=0; for(j=1, #a, if(a[1, j]%3==2&&a[2, j]%2==1, has=1; break)); if(has==0, print(i" -\t"a[1, ])))
%Y Cf. A000051, A000978, A215800.
%K nonn
%O 1,1
%A _V. Raman_, Aug 23 2012
%E 9 more terms from _V. Raman_, Aug 28 2012